Radiation from the sun keeps us alive, but with the thinning of the ozone layer, it is important to limit exposure. Most of us know that the sun is far more intense at the equator than at the poles. The relationship between the intensity of radiation with respect to the distance from the sun is given by I = k/d^2, where I represents radiation intensity in watts per square metre (w/m^2), and distance, d, in astronomical units (AU). K is a proportional constant. (The earth is 1 AU from the sun)
a) Knowing the intensity f radiation from the sun is 9140 w/m^2 on Mercury, 0.387 AU away, determine an equation relating radiation intensity and distance from the sun.
b) sketch a graph of this relationship.
a) To determine an equation relating radiation intensity and distance from the sun, we can use the given relationship I = k/d^2 and the information provided for Mercury's radiation intensity and distance from the sun.
Given:
Intensity on Mercury (I) = 9140 w/m^2
Distance from the sun to Mercury (d) = 0.387 AU
Substituting these values into the equation, we get:
9140 = k/0.387^2
To find the value of k, we can rearrange the equation as follows:
k = 9140 * 0.387^2
Calculating the expression on the right side gives us:
k ≈ 1327.57
Therefore, the equation relating radiation intensity (I) and distance from the sun (d) is:
I = 1327.57/d^2
b) To sketch a graph of this relationship, we can plot the radiation intensity (I) on the y-axis and the distance from the sun (d) on the x-axis. Since the equation is I = 1327.57/d^2, as d increases, I will decrease.
The graph will be a decreasing curve, where the y-axis represents radiation intensity in watts per square meter (w/m^2), and the x-axis represents the distance from the sun in astronomical units (AU). It will start with high intensity at low distances and gradually decrease as the distance increases.